Heat output
Wood appliances produce the most heat and keep working in a power outage, but only sealed stoves and inserts deliver it efficiently. An open masonry fireplace can be a net heat loss for the house.
Gas delivers controllable, immediate heat and most millivolt models work without electricity. Electric units are supplemental: useful in a bedroom or basement, not a heat source for a house.
What your building allows
This is usually the deciding factor. Wood needs a chimney that meets current requirements, which often means relining. Gas needs a vent route within the appliance's listed limits and a gas supply. Electric needs neither, which is why it dominates condominium installations.
Work out what can be vented before you fall in love with an appliance. The order of those two steps saves a lot of disappointment.
Maintenance reality
Wood means annual sweeping, gasket and baffle service, and handling and storing fuel. Gas means an annual service visit and very little in between. Electric means dusting and the occasional component replacement.
Factor that honestly into the decision. Plenty of wood fireplaces sit unused because the fuel logistics turned out to be the part nobody enjoyed.
Where each one makes most sense
Wood suits rural and cottage properties, outage resilience, and people who genuinely want the process. Gas suits most urban and suburban homes wanting reliable heat with minimal effort.
Electric suits condominiums, bedrooms, basements, media walls and any room where venting simply cannot happen.